Bootstrap variance estimation with survey data when estimating model parameters

Abstract

When estimating model parameters from survey data, two sources of variability should normally be taken into account for inference purposes: the model that is assumed to have generated data of the finite population, and the sampling design. If the overall sampling fraction is negligible, the model variability can in principle be ignored and bootstrap techniques that track only the sampling design variability can be used. They are typically implemented by producing design bootstrap weights, often assuming that primary sampling units are selected with replacement. The model variability is often neglected in practice, but this simplification is not always appropriate. Indeed, we provide simulation results for stratified simple random sampling showing that the use of design bootstrap weights may lead to substantial underestimation of the total variance, even when finite population corrections are ignored. We propose a generalized bootstrap method that corrects this deficiency through a simple adjustment of design bootstrap weights that accounts for the model variability. We focus on models in which the observations are assumed to be mutually independent but we do not require the validity of any assumption about their model variance. The improved performance of our proposed generalized bootstrap weights over design bootstrap weights is illustrated by means of a simulation study. Our methodology is also applied to data from the Aboriginal Children Survey conducted by Statistics Canada.